This talk focuses on the invariant measure of McKean-Vlasov (MV) stochastic differential equations (SDEs) with common noise (wCN) whose coefficients depend on both the state and the measure. Using the existence of the unique solution of the corresponding stochastic partial differential equation, we give the strong/weak existence and uniqueness of the couple of the solution and its conditional distribution of the MV-SDEwCN. Then we construct a complete product measure space under given distance and an operator acting on the measure couple of the solution. By the help of the semigroup property of the operators, we establish the existence of the unique invariant measure for the solution couple of the MV-SDEwCN, whose coefficients grow polynomially. Then we establish the uniform-in-time propagation of chaos and give the convergence rate of the measure couple of one single particle and the empirical measure of the interacting particle system to the underlying invariant measure.

报告人简介：Chenggui Yuan obtained a BSc degree from Central-China Normal University in 1985, a MSc degree from Beijing Normal University in 1988, a PhD degree from Changsha Railway University (Central South University) in 1994. He was a Lecturer and an Associate Professor in Changsha Railway University from 1994 to 2000. Then he moved to UK as a PhD student in University of Strathclyde from 2000 to 2003. He was a research associate in University of Cambridge from 2003 to 2004. He moved to Swansea University as a Lecturer in 2004, then he was promoted to Senior Lecturer, Reader and Professor. His research fields are stochastic analysis, stochastic control and population dynamics. He has published more than 130 papers. He is now an Associate Editor of three international journals.